Conditional versus Marginal Covariance Representation for Linear and Nonlinear Models
DOI:
https://doi.org/10.17713/ajs.v35i1.346Abstract
Grouped data, such as repeated measures and longitudinal data, are increasingly collected in different areas of application, as varied as clinical trials, epidemiological studies, and educational testing. It is often of interest, for these data, to explore possible relationships between one or more response variables and available covariates. Because of the within-group correlation typically present with this type of data, special regression models that allow the joint estimation of mean and covariance parameters need to be used. Two main approaches have been proposed to represent the covariance structure of the data with these models: (i) via the use of random effects, the so-called conditional model and (ii) through direct representation of the covariance structure of the responses, known as the marginal approach. Here we discuss and compare these two approaches in the context of linear and non-linear regression models with additive Gaussian errors, using a real data example to motivate and illustrate the discussion.
References
Bates, D. M., andWatts, D. G. (1988). Nonlinear regression analysis and its applications. New York: Wiley.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994). Time series analysis: Forecasting and control (3rd ed.). San Francisco: Holden-Day.
Davidian, M., and Gallant, A. R. (1992). Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to quinidine. Journal of Pharmacokinetics and Biopharmaceutics, 20, 529–556.
Davidian, M., and Giltinan, D. M. (1995). Nonlinear models for repeated measurement data. London: Chapman & Hall.
Jennrich, R. I., and Schluchter, M. D. (1986). Unbalanced repeated measures models with structural covariance matrices. Biometrics, 42(4), 805–820.
Laird, N. M., and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963–974.
Lindstrom, M. J., and Bates, D. M. (1990). Nonlinear mixed-effects models for repeated measures data. Biometrics, 46, 673–687.
Littell, R. C., Milliken, G. A., Stroup,W.W., andWolfinger, R. D. (1996). Sas system for mixed models. Cary, NC: SAS Institute Inc.
Mallet, A., Mentre, F., Steimer, J.-L., and Lokiek, F. (1988). Nonparametric maximum likelihood estimation for population pharmacokinetics, with applications to
Cyclosporine. Journal of Pharmacokinetics and Biopharmaceutics, 16, 311–327.
Pinheiro, J. C., and Bates, D. M. (2000). Mixed-effects models in S and S-PLUS. New York: Springer-Verlag.
Ramos, R. Q., and Pantula, S. G. (1995). Estimation of nonlinear random coefficient models. Statistics & Probability Letters, 24, 49–56.
Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance components. New York: Wiley.
Sheiner, L. B., and Beal, S. L. (1980). Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis–Menten model: Routine clinical
pharmacokinetic data. Journal of Pharmacokinetics and Biopharmaceutics, 8(6), 553–571.
Vonesh, E. F., and Carter, R. L. (1992). Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics, 48, 1–18.
Vonesh, E. F., and Chinchilli, V. M. (1997). Linear and nonlinear models for the analysis of repeated measures. New York: Marcel Dekker.
Wakefield, J. C., Smith, A. F. M., Racine-Poon, A., and Gelfand, A. E. (1994). Bayesian analysis of linear and nonlinear population models using the Gibbs sampler. Applied Statistics, 43, 201–221.
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